%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM394+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 09:32:05 EDT 2022
% Result : Theorem 0.22s 1.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 13 unt; 0 def)
% Number of atoms : 130 ( 7 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 139 ( 57 ~; 57 |; 12 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 71 ( 5 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t26_ordinal1,conjecture,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ordinal_subset(X1,X2)
| in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t26_ordinal1) ).
fof(connectedness_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',connectedness_r1_ordinal1) ).
fof(redefinition_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_r1_ordinal1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t3_subset) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t4_subset) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t5_subset) ).
fof(t24_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t24_ordinal1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_subset) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',antisymmetry_r2_hidden) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',reflexivity_r1_tarski) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ordinal_subset(X1,X2)
| in(X2,X1) ) ) ),
inference(assume_negation,[status(cth)],[t26_ordinal1]) ).
fof(c_0_11,plain,
! [X3,X4] :
( ~ ordinal(X3)
| ~ ordinal(X4)
| ordinal_subset(X3,X4)
| ordinal_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1])]) ).
fof(c_0_12,negated_conjecture,
( ordinal(esk1_0)
& ordinal(esk2_0)
& ~ ordinal_subset(esk1_0,esk2_0)
& ~ in(esk2_0,esk1_0) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])]) ).
cnf(c_0_13,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
ordinal(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X3,X4] :
( ( ~ ordinal_subset(X3,X4)
| subset(X3,X4)
| ~ ordinal(X3)
| ~ ordinal(X4) )
& ( ~ subset(X3,X4)
| ordinal_subset(X3,X4)
| ~ ordinal(X3)
| ~ ordinal(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
cnf(c_0_16,negated_conjecture,
( ordinal_subset(esk2_0,X1)
| ordinal_subset(X1,esk2_0)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
ordinal(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
~ ordinal_subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_19,plain,
! [X3,X4,X3,X4] :
( ( ~ element(X3,powerset(X4))
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| element(X3,powerset(X4)) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])])]) ).
cnf(c_0_20,plain,
( subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
ordinal_subset(esk2_0,esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
fof(c_0_22,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| element(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
cnf(c_0_23,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
subset(esk2_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_14]),c_0_17])]) ).
fof(c_0_25,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| ~ empty(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(c_0_26,plain,
! [X3,X4] :
( ~ ordinal(X3)
| ~ ordinal(X4)
| in(X3,X4)
| X3 = X4
| in(X4,X3) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t24_ordinal1])])])])])]) ).
fof(c_0_27,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_28,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
element(esk2_0,powerset(esk1_0)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( in(X1,X2)
| X2 = X1
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( element(X1,esk1_0)
| ~ in(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( ~ empty(esk1_0)
| ~ in(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( X1 = esk2_0
| in(esk2_0,X1)
| in(X1,esk2_0)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_14]) ).
cnf(c_0_36,negated_conjecture,
~ in(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_37,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ in(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden])])]) ).
cnf(c_0_38,negated_conjecture,
( in(X1,esk1_0)
| ~ in(X1,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( esk2_0 = esk1_0
| in(esk1_0,esk2_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_17]),c_0_36]) ).
cnf(c_0_40,plain,
( ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_41,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( esk2_0 = esk1_0
| in(esk1_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_43,plain,
! [X3] : subset(X3,X3),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_44,negated_conjecture,
~ subset(esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_40]),c_0_17]),c_0_14])]) ).
cnf(c_0_45,negated_conjecture,
esk2_0 = esk1_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_42]) ).
cnf(c_0_46,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM394+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jul 7 17:02:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.22/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.41 # Preprocessing time : 0.016 s
% 0.22/1.41
% 0.22/1.41 # Proof found!
% 0.22/1.41 # SZS status Theorem
% 0.22/1.41 # SZS output start CNFRefutation
% See solution above
% 0.22/1.41 # Proof object total steps : 48
% 0.22/1.41 # Proof object clause steps : 27
% 0.22/1.41 # Proof object formula steps : 21
% 0.22/1.41 # Proof object conjectures : 20
% 0.22/1.41 # Proof object clause conjectures : 17
% 0.22/1.41 # Proof object formula conjectures : 3
% 0.22/1.41 # Proof object initial clauses used : 14
% 0.22/1.41 # Proof object initial formulas used : 10
% 0.22/1.41 # Proof object generating inferences : 12
% 0.22/1.41 # Proof object simplifying inferences : 13
% 0.22/1.41 # Training examples: 0 positive, 0 negative
% 0.22/1.41 # Parsed axioms : 36
% 0.22/1.41 # Removed by relevancy pruning/SinE : 12
% 0.22/1.41 # Initial clauses : 36
% 0.22/1.41 # Removed in clause preprocessing : 0
% 0.22/1.41 # Initial clauses in saturation : 36
% 0.22/1.41 # Processed clauses : 89
% 0.22/1.41 # ...of these trivial : 0
% 0.22/1.41 # ...subsumed : 9
% 0.22/1.41 # ...remaining for further processing : 80
% 0.22/1.41 # Other redundant clauses eliminated : 0
% 0.22/1.41 # Clauses deleted for lack of memory : 0
% 0.22/1.41 # Backward-subsumed : 1
% 0.22/1.41 # Backward-rewritten : 27
% 0.22/1.41 # Generated clauses : 87
% 0.22/1.41 # ...of the previous two non-trivial : 88
% 0.22/1.41 # Contextual simplify-reflections : 4
% 0.22/1.41 # Paramodulations : 87
% 0.22/1.41 # Factorizations : 0
% 0.22/1.41 # Equation resolutions : 0
% 0.22/1.41 # Current number of processed clauses : 52
% 0.22/1.41 # Positive orientable unit clauses : 15
% 0.22/1.41 # Positive unorientable unit clauses: 0
% 0.22/1.41 # Negative unit clauses : 2
% 0.22/1.41 # Non-unit-clauses : 35
% 0.22/1.41 # Current number of unprocessed clauses: 26
% 0.22/1.41 # ...number of literals in the above : 63
% 0.22/1.41 # Current number of archived formulas : 0
% 0.22/1.41 # Current number of archived clauses : 28
% 0.22/1.41 # Clause-clause subsumption calls (NU) : 207
% 0.22/1.41 # Rec. Clause-clause subsumption calls : 155
% 0.22/1.41 # Non-unit clause-clause subsumptions : 13
% 0.22/1.41 # Unit Clause-clause subsumption calls : 68
% 0.22/1.41 # Rewrite failures with RHS unbound : 0
% 0.22/1.41 # BW rewrite match attempts : 4
% 0.22/1.41 # BW rewrite match successes : 2
% 0.22/1.41 # Condensation attempts : 0
% 0.22/1.41 # Condensation successes : 0
% 0.22/1.41 # Termbank termtop insertions : 2826
% 0.22/1.41
% 0.22/1.41 # -------------------------------------------------
% 0.22/1.41 # User time : 0.016 s
% 0.22/1.41 # System time : 0.004 s
% 0.22/1.41 # Total time : 0.021 s
% 0.22/1.41 # Maximum resident set size: 2992 pages
%------------------------------------------------------------------------------